On the linear elasticity of porous materials

In this work, a porous material is represented as a composite made of an isotropic matrix and spheroidal inclusions with zero stiffness, describing the pores. The shape of the pores ranges from flat to spherical to fibre-like, and their orientation is assumed to obey a given probability distribution function. As an example of straightforward physical interpretation, the isotropic case of randomly oriented voids-pores is studied as a function of the matrix Poisson's ratio and the porosity (void volumetric fraction). The results are in good agreement with published experimental data on porous metals, and with previous isotropic solutions in the literature.